Perform the indicated operation and simplify the result. Leave your answer in factored form. (5x+20)/(8x^(5) )·(x)/(x^(2) -16)

Question

Perform the indicated operation and simplify the result. Leave your answer in factored form.


`(5x+20)/(8x^(5) )`·
`(x)/(x^(2) -16)`

Answer 1

First, you have to factorize the expressions :

`\frac{5x + 20}{8 {x}^(5) } * \frac{x}{ {x}^(2) - 16}`

`= \frac{5(x + 4)}{8 {x}^(5) } * (x)/((x + 4)(x - 4))`

Second, you have to cross out the similar expressions :

`= \frac{5}{8 {x}^(5) } * (x)/((x - 4))`

Third, you have to multiply both fractions :

`= \frac{5x}{8 {x}^(5)(x - 4) }`

Lastly, you have to simplify :

`= \frac{5}{8 {x}^(4)(x - 4) }`